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Arsdigita 02 Discrete Mathematics Lecture 1720
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Course 02: Discrete Mathematics (Arsdigita University) • • This course covers the mathematical topics most directly related to computer science. Topics include: logic, relations, functions, basic set theory, countability and counting arguments, proof techniques, mathematical induction, graph theory, combinatorics, discrete probability, recursion, recurrence relations, and number theory. Emphasis is placed on providing a context for the application of the mathematics within computer science. • • Instructor: Shai Simonson • • Text: Discrete Mathematics and its Applications, Rosen. • • 01 What kinds of problems are solved in discrete math? • • 02 Boolean Algebra and formal logic • • 03 More logic: quantifiers and predicates • • 04 Sets • • 05 Diagonalization, functions and sums review • • 06 Basic arithmetic and geometric sums, closed forms. • • 07 Chinese rings puzzle • • 08 Solving recurrence equations • • 09 Solving recurrence equations (cont.) • • 10 Mathematical induction • • 11 Combinations and permutations • • 12 Counting Problems • • 13 Counting problems • • 14 Counting problems using combinations, distributions • • 15 Counting problems using combinations, distributions • • 16 The pigeonhole principle and examples. The inclusion/exclusion theorem and advanced examples. A combinatorial card trick. • • 17 Equivalence Relations and Partial Orders • • 18 Euclid's Algorithm • • 19 Recitation -- a combinatorial card trick • • 20 Cryptography • • • More information about this course: http://www.archive.org/details/arsdig... http://www.aduni.org/courses/discrete • • Licensed under Creative Commons Attribution ShareAlike 2.0: http://www.aduni.org/FAQ/#redist1 http://creativecommons.org/licenses/b... • ArsDigita
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